Answer:
The correct option is A.
Step-by-step explanation:
Let the distance between the zoo and the library is x.
In a right angled triangle,
[tex]\tan \theta = \frac{opposite}{adjacent}[/tex]
In triangle ABG,
[tex]\tan (30^{\circ}) = \frac{AG}{GB}[/tex]
[tex]\frac{1}{\sqrt{3}} = \frac{200\sqrt{3}}{GB}[/tex]
On cross multiplication, we get
[tex]GB\times 1=\sqrt{3}\times 200\sqrt{3}[/tex]
[tex]GB=600[/tex]
In triangle AGC,
[tex]\tan (60^{\circ}) = \frac{AG}{GC}[/tex]
[tex]\sqrt{3} = \frac{200\sqrt{3}}{GC}[/tex]
On cross multiplication, we get
[tex]GC\times \sqrt{3}=200\sqrt{3}[/tex]
Divide both sides by √3.
[tex]GC=200[/tex]
The distance between the zoo and the library is
[tex]CB=GB-GC[/tex]
[tex]x=600-200[/tex]
[tex]x=400[/tex]
The distance between the zoo and the library is 400 feet. Therefore the correct option is A.
